Alternating Weighted Sums of Inverses of Binomial Coefficients

Renzo Sprugnoli Dipartimento di Sistemi e Informatica Viale Morgagni 65 50134 Firenze Italy

               renzo.sprugnoli@unifi.it

Abstract

We consider the alternating sums S_{n}^{(m)} = ∑_{k=0}^{n}(−1)^{n−k}k^{m}\binom{n}{k}^{−1}, recently studied by Belbachir, Rahmani, and Sury, and obtain some results complementary to those found by the three authors, especially for what concerns generating functions, closed forms and asymptotic approximation.

1 Introduction